Find the Domain y=5/(2x+24)

$y = \frac{5}{2 x + 24}$

Step 1

Set the denominator in $\frac{5}{2 x + 24}$ equal to $0$ to find where the expression is undefined.

$2 x + 24 = 0$

Step 2

Solve for $x$ .

Subtract $24$ from both sides of the equation.

$2 x = - 24$

Divide each term in $2 x = - 24$ by $2$ and simplify.

Divide each term in $2 x = - 24$ by $2$ .

$\frac{2 x}{2} = \frac{- 24}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 24}{2}$

Divide $x$ by $1$ .

$x = \frac{- 24}{2}$

Simplify the right side.

Divide $- 24$ by $2$ .

$x = - 12$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, - 12) \cup (- 12, \infty)$

Set-Builder Notation:

${x | x \neq - 12}$

Step 4